Absolute Molecular Orientational Distribution of the Polystyrene Surface

Orientation difference of chemically immobilized and physically adsorbed biological molecules on polymers detected at the solid/liquid interfaces in situ

A surface sensitive second order nonlinear optical technique, sum frequency generation vibrational spectroscopy, was applied to study peptide orientation on polymer surfaces, supplemented by a linear vibrational spectroscopy, attenuated total reflectance Fourier transform infrared spectroscopy. Using the antimicrobial peptide Cecropin P1 as a model system, we have quantitatively demonstrated that chemically immobilized peptides on polymers adopt a more ordered orientation than less tightly bound physically adsorbed peptides. These differences were also observed in different chemical environments, for example, air versus water. Although numerous studies have reported a direct correlation between the choice of immobilization method and the performance of an attached biological molecule, the lack of direct biomolecular structure and orientation data has made it difficult to elucidate the relationship between structure, orientation, and function at a surface. In this work, we directly studied the effect of chemical immobilization method on biomolecular orientation/ordering, an important step for future studies of biomolecular activity. The methods for orientation analysis described within are also of relevance to understanding biosensors, biocompatibility, marine-antifouling, membrane protein functions, and antimicrobial peptide activities.

Deducing 2D crystal structure at the liquid/solid interface with atomic resolution: a combined STM and SFG study

Sum frequency generation vibrational spectroscopy (SFG) has been applied to study two-dimensional (2D) crystals formed by an isophthalic acid diester on the surface of highly oriented pyrolytic graphite, providing complementary measurements to scanning tunneling microscopy (STM) and computational modeling. SFG results indicate that both aromatic and C=O groups in the 2D crystal tilt from the surface. This study demonstrates that a combination of SFG and STM techniques can be used to gain a more complete picture of 2D crystal structure, and it is necessary to consider solvent-2D crystal interactions and dynamics in the computer models to achieve an accurate representation of interfacial structure.

In situ molecular level studies on membrane related peptides and proteins in real time using sum frequency generation vibrational spectroscopy

Sum frequency generation (SFG) vibrational spectroscopy has been demonstrated to be a powerful technique to study the molecular structures of surfaces and interfaces in different chemical environments. This review summarizes recent SFG studies on hybrid bilayer membranes and substrate-supported lipid monolayers and bilayers, the interaction between peptides/proteins and lipid monolayers/bilayers, and bilayer perturbation induced by peptides/proteins. To demonstrate the ability of SFG to determine the orientations of various secondary structures, studies on the interactions between different peptides/proteins (melittin, G proteins, alamethicin, and tachyplesin I) and lipid bilayers are discussed. Molecular level details revealed by SFG in these studies show that SFG can provide a unique understanding on the interactions between a lipid monolayer/bilayer and peptides/proteins in real time, in situ and without any exogenous labeling.

Surface segregation of fluorinated moieties on random copolymer films controlled by random-coil conformation of polymer chains in solution

The relationship between solution properties, film-forming methods, and the solid surface structures of random copolymers composed of butyl methacrylate and dodecafluorheptyl methylacrylate (DFHMA) was investigated by contact angle measurements, X-ray photoelectron spectroscopy, sum frequency generation vibrational spectroscopy, and surface tension measurements. The results, based on thermodynamic considerations, demonstrated that the random copolymer chain conformation at the solution/air interface greatly affected the surface structure of the resulting film, thereby determining the surface segregation of fluorinated moieties on films obtained by various film-forming techniques. When the fluorinated monomer content of the copolymer solution was low, entropic forces dominated the interfacial structure, with the perfluoroalkyl groups unable to migrate to the solution/air interface and thus becoming buried in a random-coil chain conformation. When employing this copolymer solution for film preparation by spin-coating, the copolymer chains in solution were likely extended due to centrifugal forces, thereby weakening the entropy effect of the polymer chains. Consequently, this resulted in the segregation of the fluorinated moieties on the film surface. For the films prepared by casting, the perfluoroalkyl groups were, similar to those in solution, incapable of segregating at the film surface and were thus buried in the random-coil chains. When the copolymers contained a high content of DFHMA, the migration of perfluoroalkyl groups at the solution/air interface was controlled by enthalpic forces, and the perfluoroalkyl groups segregated at the surface of the film regardless of the film-forming technique. The aim of the present work was to obtain an enhanced understanding of the formation mechanism of the chemical structure on the surface of the polymer film, while demonstrating that film-forming methods may be used in practice to promote the segregation of fluorinated moieties on film surfaces.

Probing molecular-level surface structures of polyethersulfone/pluronic F127 blends using sum-frequency generation vibrational spectroscopy

We blended Pluronic F127 into polyethersulfone (PES) to improve surface properties of PES, which has been extensively used in biomaterial and other applications. The molecular surface structures of PES/Pluronic F127 blends have been investigated by sum-frequency generation (SFG) vibrational spectroscopy. The molecular orientation of surface functional groups of PES changed significantly when blended with a small amount of Pluornic F127. Pluronic F127 on the blend surface also exhibited different features upon contacting with water. The entanglement of PES chains with Pluronic F127 molecules rendered the blends with long-term surface stability in water in contrast to the situation where a layer of Pluronic F127 adsorbed on the PES surface. Atomic force microscopy (AFM) and quartz crystal microbalance (QCM) measurements were included to determine the relative amount of protein that adsorbed to the blend surfaces. The results showed a decreased protein adsorption amount with increasing Pluronic F127 bulk concentration. The correlations between polymer surface properties and detailed molecular structures obtained by SFG would provide insight into the designing and developing of biomedical polymers and functional membranes with improved fouling-resistant properties.

Systematic oxidation of polystyrene by ultraviolet-ozone, characterized by near-edge X-ray absorption fine structure and contact angle

The process of implanting oxygen in polystyrene (PS) via exposure to ultraviolet-ozone (UV-O) was systematically investigated using the characterization technique of near-edge X-ray absorption fine structure (NEXAFS). Samples of PS exposed to UV-O for 10-300 s and washed with isopropanol were analyzed using the carbon and oxygen K-edge NEXAFS partial electron yields, using various retarding bias voltages to depth-profile the oxygen penetration into the surface. Evaluation of reference polymers provided a scale to quantify the oxygen concentration implanted by UV-O treatment. We find that ozone initially reacts with the double bonds on the phenyl rings, forming carbonyl groups, but within 1 min of exposure, the ratio of double to single oxygen bonds stabilizes at a lower value. Oxygen penetrates the film with relative ease, creating a fairly uniform distribution of oxygen within at least the first 4 nm (the effective depth probed by NEXAFS here). Before oxygen accumulates in large concentrations, however, it preferentially degrades the uppermost layer of the film by removing oxygenated low-molecular-weight oligomers. The failure to accumulate high concentrations of oxygen is seen in the nearly constant carbon edge jump, the low concentration of oxygen even at 5 min exposure (58% of that in poly(4-acetoxystyrene), the polymer with the most similarities to UV-O-treated PS), and the relatively high contact angles. At 5 min exposure the oxygen concentration contains ca. 7 atomic % oxygen. The oxygen species that are implanted consist predominantly of single O-C bonds and double O=C bonds but also include a small fraction of O-H. UV-O treatment leads a plateau after 2 min exposure in the water contact angle hysteresis, at a value of 67 +/- 2 degrees , due primarily to chemical heterogeneity. Annealing above T(g) allows oxygenated species to move short distances away from the surface but not diffuse further than 1-2 nm.

Structural information of mussel adhesive protein Mefp-3 acquired at various polymer/Mefp-3 solution interfaces

Mytilus edulis foot protein Mefp-3 serves as a primer in the formation of adhesive plaques that attach the mussel to solid surfaces in its immediate environment. The adsorption behavior of this protein on various materials of different hydrophobicity was studied using sum frequency generation (SFG) vibrational spectroscopy. By collecting SFG signals from side chains of these amino acids and from secondary structures of the protein, we have determined that this protein adopts different conformations at different interfaces, depending on hydrophobicity of the contact medium and specific chemical group interactions. We have also demonstrated that SFG has the potential to track the interfacial conformations of a single amino acid in a protein.

Diffusion of one or more components of a silane adhesion-promoting mixture into poly(methyl methacrylate)

The surface-sensitive technique of sum frequency generation (SFG) vibrational spectroscopy has been applied to study the buried interfaces between different polymers including deuterated polystyrene (d-PS) and deuterated poly(methyl methacrylate) (d-PMMA) and a two-component silane adhesion-promoting mixture (SAPM) composed of (3-glycidoxypropyl)trimethoxysilane (gamma-GPS) and a methylvinylsiloxanol (MVS). Because of the dissolution of d-PS, no SFG CH stretching signals could be collected from the d-PS/gamma-GPS interface, and SFG signals collected from the d-PS/SAPM interface gradually disappeared over time. SFG results also showed that gamma-GPS can diffuse through the d-PMMA film. The diffusion of gamma-GPS through the d-PMMA film was confirmed by SFG studies on the interface between gamma-GPS and a d-PMMA/PS two-polymer layer system. Initially the SFG signal from the PS layer was detected. However, after gamma-GPS diffused through the d-PMMA film, the PS film was dissolved by the silane, and thus the SFG signal from PS was lost. Similar experiments have been carried out at the interface between the SAPM and the d-PMMA/PS two-polymer layer system and it was found that the diffusion time of the gamma-GPS in the SAPM through the d-PMMA film was significantly longer. These results were much different to those from previous SFG studies on the analogous PET interfaces and appear consistent with differences in solubility parameters calculated for these systems.

Detection and Spectral Analysis of Trifluoromethyl Groups at a Surface by Sum Frequency Generation Vibrational Spectroscopy

Sum frequency generation (SFG) vibrational spectroscopy was used to detect the presence of trifluoromethyl groups on the surface of 4-(trifluoromethyl)benzyl alcohol (TFMBA) in air. Supplementary data from infrared and Raman spectra were correlated to ab initio calculations by use of density functional theory (DFT) for TFMBA and three related compounds to reliably assign vibrational modes to the spectra. It was shown that strongly ordered CF3 groups dominate the surface of the TFMBA, and the vibrational modes of this functional group are strongly coupled to the benzene ring of the benzyl alcohol. This coupling, along with the SFG activity of the CF3 group, is removed with the insertion of an oxygen atom between the CF3 group and the benzene ring.

Molecular orientation and alignment of rubbed poly(vinyl cinnamate) surfaces

We observed that weakly and strongly rubbed polyvinyl-cinnamate surfaces align liquid crystal films perpendicular and parallel to the rubbing direction, respectively. Surface-specific sum-frequency vibrational spectroscopy was used to probe molecular orientations and alignments of the rubbed surfaces and provide a molecular-level understanding of the observation.

Surface vibrational structure at alkane liquid/vapor interfaces

Broadband vibrational sum frequency spectroscopy (VSFS) has been used to examine the surface structure of alkane liquid/vapor interfaces. The alkanes range in length from n-nonane (C(9)H(20)) to n-heptadecane (C(17)H(36)), and all liquids except heptadecane are studied at temperatures well above their bulk (and surface) freezing temperatures. Intensities of vibrational bands in the CH stretching region acquired under different polarization conditions show systematic, chain length dependent changes. Data provide clear evidence of methyl group segregation at the liquid/vapor interface, but two different models of alkane chain structure can predict chain length dependent changes in band intensities. Each model leads to a different interpretation of the extent to which different chain segments contribute to the anisotropic interfacial region. One model postulates that changes in vibrational band intensities arise solely from a reduced surface coverage of methyl groups as alkane chain length increases. The additional methylene groups at the surface must be randomly distributed and make no net contribution to the observed VSF spectra. The second model considers a simple statistical distribution of methyl and methylene groups populating a three dimensional, interfacial lattice. This statistical picture implies that the VSF signal arises from a region extending several functional groups into the bulk liquid, and that the growing fraction of methylene groups in longer chain alkanes bears responsibility for the observed spectral changes. The data and resulting interpretations provide clear benchmarks for emerging theories of molecular structure and organization at liquid surfaces, especially for liquids lacking strong polar ordering.

Broadband coherent anti-Stokes Raman spectroscopy characterization of polymer thin films

Broadband coherent anti-Stokes Raman spectroscopy (CARS) is demonstrated as an effective probe of polymer thin film materials. A simple modification to a 1 kHz broad bandwidth sum frequency generation (SFG) spectrometer permits acquisition of CARS spectra for polymer thin films less than 100 nm thick, a dimension relevant to organic electronic device applications. CARS spectra are compared to the conventional Raman spectra of polystyrene and the resonance-enhanced Raman spectra of poly(3-hexylthiophene). The CARS spectra obtained under these conditions consistently demonstrate enhanced signal-to-noise ratio compared to the spontaneous Raman scattering. The sensitivity of the CARS measurement is limited by the damage threshold of the samples. The dielectic properties of the substrate have a dramatic effect on the detected signal intensity. For ultrathin films, the strongest signals are obtained from fused silica surfaces. Similar to surface-enhanced Raman scattering (SERS), Au also gives a large signal, but contrary to SERS, no surface roughening is necessary.

Examination of glass transitions in CO(2)-processed, peracetylated sugars using sum frequency generation spectroscopy

The present study utilizes vibrational sum frequency generation (SFG) spectroscopy to study changes in the surface crystallinity of various peracetylated sugars, a class of materials that have a high affinity for carbon dioxide (CO(2)). Studies of the solid-air interface of acetylated beta-cyclodextrin (Ac-beta-CD) and sucrose octaacetate (SOA) show that diffuse reflectance SFG spectroscopy is sensitive to changes in crystallinity from processing with either heat or solvation in CO(2), due to the loss of signal after glassification occurs. beta-d-Glucose pentaacetate (Ac-beta-GLC) was used as a control for this experiment due to the fact that it does not undergo a crystalline phase transition, regardless of processing conditions. The crystalline to amorpohous transitions of these bulk materials were verified using differential scanning calorimetry (DSC) as a function of thermal and CO(2) processing. In addition, preliminary results suggest that the SFG technique is sensitive in detecting the degree of crystallinity at the interface as a result of incomplete processing and presents new opportunities for the examination and detection of surface crystallinity changes.

Rubbing-induced anisotropy of long alkyl side chains at polyimide surfaces

Molecular organization at polyimide surfaces used as alignment layers in liquid crystal displays was investigated using vibrational sum frequency generation (SFG) spectroscopy. We focus on the orientation of the long alkyl side groups at the polymer surface using polarization-selected SFG spectra of the CH(3)- and CH(2)-stretch modes of the side chain. Mechanical rubbing and baking, an accepted industrial procedure used to produce pretilt of the liquid crystal, was found to induce pronounced azimuthal anisotropy in the orientational distribution of the alkyl side chains. Orientational analysis of the SFG vibrational spectra in terms of the azimuthal and tilt angles (in and out of plane, respectively) of the alkyl side chains shows their preferential tilt along the rubbing direction, with the azimuthal distribution narrower for stronger rubbed polymer samples.

Irreducible representation and projection operator application to understanding nonlinear optical phenomena: hyper-Raman, sum frequency generation, and four-wave mixing spectroscopy

Symmetry plays an essential role in understanding optical activities of a molecule in infrared and Raman vibrational spectroscopy as well as in nonlinear optical vibrational spectroscopy. Each vibrational mode belongs to an irreducible representation of the underlying symmetry group. In this paper, using the alpha-helical polypeptide symmetry as an example, we calculate all the third rank nonzero hyper-Raman tensors as well as the infrared and Raman tensors by applying the projection operators to each irreducible species. We demonstrate that the projection operator method provides selection rules for the infrared, Raman, and hyper-Raman vibrational transitions and also other nonlinear optical spectroscopy such as sum frequency generation and the four-, five-, and six-wave mixing coherent vibrational transitions. Specific expressions for all nonzero elements of the corresponding nonlinear susceptibility tensors in a laboratory-fixed coordinate frame are also deduced.

Sum Frequency Generation Vibrational Spectroscopic Studies on a Silane Adhesion-Promoting Mixture at a Polymer Interface

Sum frequency generation (SFG) vibrational spectroscopy was used to probe the interface between poly(ethylene terephthalate) with deuterated ethylene glycol subunits (d4-PET) and a silane adhesion-promoting mixture (SAPM) comprised of (3-glycidoxypropyl)trimethoxysilane (gamma-GPS) and a methylvinylsiloxanol (MVS). Such a mixture has been found to improve the adhesion of an addition-curing silicone elastomer to a range of plastic and metal substrates. Our results demonstrated that at the interface between d4-PET and a SAPM with a gamma-GPS/MVS ratio of 1:1 (w/w), the silane molecules not only segregated to the interface but also the methoxy headgroups likely adopted a greater net orientational order along the surface normal than at the d4-PET/gamma-GPS interface. The effects of varying the silane/siloxane ratio and using different siloxane oligomers on interfacial structures were also examined. This study provides unique molecular-level insights into the prerequisite conditions for adhesion of curable silicone adhesives.

Entropically Mediated Polyolefin Blend Segregation at Buried Sapphire and Air Interfaces Investigated by Infrared−Visible Sum Frequency Generation Vibrational Spectroscopy

The segregation behavior of binary polymer blends at hydrophilic solid sapphire and air interfaces was investigated by infrared-visible sum frequency generation (SFG) vibrational spectroscopy. SFG spectra were collected from a bulk miscible blend consisting of identical molecular weight (approximately 54,000) and similar surface free energy (29-35 dyn/cm) components of atactic polypropylene (aPP) and aspecific poly(ethylene-co-propylene) rubber (aEPR). Characteristic CH resonances of the blend were contrasted with those of the individual components at both buried (sapphire/polymer) and free (air/polymer) interfaces. Preferential segregation of the aPP component was observed after annealing at both air/polymer and sapphire/polymer interfaces. SFG spectra revealed ordering of the polymer backbone segments with the methylene (CH2) groups perpendicular to the surface at the sapphire interface and the methyl (CH3) groups upright at the air interface. The SFG results indicate that the surface composition can be determined from the peak intensities that are characteristic of each component and that conformational entropy played a likely role in surface segregation. aPP occupied a smaller free volume at the surface because of a statistically smaller segment length (aPP is more flexible and has a shorter length). In addition, the high density of the ordered CH3 side branches enhanced the surface activity by allowing the long-chain backbone segments of aPP to order at the surface.

Computational steering in Monte Carlo simulations of thin film polystyrene

High molecular weight polymer systems show very long relaxation times, of the order of milliseconds or more. This time-scale proves practically inaccessible for atomic-scale dynamical simulation such as molecular dynamics. Even with a Monte Carlo (MC) simulation, the generation of statistically independent configurations is non-trivial. Many moves have been proposed to enhance the efficiency of MC simulation of polymers. Each is described by a proposal density Q(x'; x): the probability of selecting the trial state x' given that the system is in the current state x. This proposal density must be parametrized for a particular chain length, chemistry and temperature. Choosing the correct set of parameters can greatly increase the rate at which the system explores its configuration space. Computational steering (CS) provides a new methodology for a systematic search to optimize the proposal densities for individual moves, and to combine groups of moves to greatly improve the equilibration of a model polymer system. We show that monitoring the correlation time of the system is an ideal single parameter for characterizing the efficiency of a proposal density function, and that this is best evaluated by a distributed network of replicas of the system, with the operator making decisions based on the averages generated over these replicas. We have developed an MC code for simulating an anisotropic atomistic bead model which implements the CS paradigm. We report simulations of thin film polystyrene.

Surface Structures and Properties of Polystyrene/Poly(methyl methacrylate) Blends and Copolymers

Sum frequency generation (SFG) vibrational spectroscopy has been applied to study the molecular surface structures of polystyrene (PS)/poly(methyl methacrylate) (PMMA) blends and the copolymer between PS and PMMA (PS-co-PMMA) in air, supplemented by atomic force microscopy (AFM) and contact angle goniometer. Both the blend and the copolymer have equal weight amounts of the two components. SFG results show that both components, PS and PMMA, can segregate to the surface of the blend and the copolymer before annealing, although PMMA has a slightly higher surface tension. Upon annealing both SFG results and contact angle measurements indicate that the PS segregates to the surface of the PS/PMMA blend more but no change occurs on the PS-co-PMMA surface. AFM images show that the copolymer surface is flat but the 1:1 PS/PMMA blend has a rougher surface with island like domains present. The annealing effect on the blend surface morphology has also been investigated. We collected amide SFG signals from interfacial fibrinogen molecules at the copolymer or blend/protein solution interfaces as a function of time. Different time-dependent SFG signal changes have been observed, showing that different surfaces of the blend and the copolymer mediate fibrinogen adsorption behavior differently.

Molecular composition and mechanical properties of biopolymer interfaces studied by sum frequency generation vibrational spectroscopy and atomic force microscopy

Sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM) have been used to study the surface structure and surface mechanical behavior of biologically-relevant polymer systems. These techniques have emerged as powerful surface analytical tools to deduce structure/property relationships in situ, at both air/solid and air/liquid interfaces. SFG and AFM studies have been performed to understand how the surface properties of polymers are linked to polymer bulk compositions, changes in the ambient environment, or the degree of mechanical strain. Specifically, this review discusses (1) the macroscopic- and molecular-level tracking of small end groups attached to polyurethane blends, engineered to reduce blood clotting; (2) the role of ambient humidity on the surface mechanics of soft contact lenses possessing different water content in the bulk; (3) the affect of cyclic stretch on the molecular surface structure of polyurethane films, designed to mimic the mechanical deformation caused by heartbeat; and (4) the molecular ordering of functional groups at the polystyrene-protein interface. The correlation of spectroscopic and mechanical data by SFG and AFM is a powerful methodology to study and design materials with tailored surface properties.

Effect of rubbing-induced polymer chain alignment on adhesion and friction of glassy polystyrene surfaces

The friction and adhesion properties of polystyrene surfaces are studied below the glass transition temperature by means of atomic force microscopy in argon. Even at a temperature far below the glass transition, the repeated sliding of a polystyrene bead tip on the non-cross-linked polystyrene surface causes significant reduction of friction and adhesion forces. There is no measurable wear of the polystyrene surface due to repeated sliding. These decreases are associated with the alignment of the outermost polymer segments induced by repeated rubbing. There are only little changes in friction and adhesion on the cross-linked polystyrene surface in which the covalent cross-linking prevents chain realignment.

Piperidine adsorption on hydrated alpha-alumina (0001) surface studied by vibrational sum frequency generation spectroscopy

The adsorption of piperidine vapor on the hydrated alumina (alpha-Al2O3, corundum) (0001) surface was investigated using vibrational broad bandwidth and scanning sum frequency generation (SFG) spectroscopy. The interfacial vibrational signature in the C-H stretching region of piperidine at the alumina (0001) surface is shown to be a sensitive spectroscopic probe revealing the adsorption mechanism. The neat piperidine surface, aqueous piperidine surface, and aqueous piperidium chloride surface were also investigated in the C-H stretching region by SFG to establish vibrational reference frequencies. After piperidine adsorption, piperidine vapor was removed and piperidine was found to be chemisorbed onto the alumina (0001) surface through protonation by surface hydroxyl groups. The O-H stretching region of the alumina surface before and after piperidine adsorption was also investigated, and the results revealed the decrease of the surface number density of alumina surface hydroxyl groups.

Sum frequency generation studies at poly(ethylene terephthalate)/silane interfaces: hydrogen bond formation and molecular conformation determination

To better understand the effects of interfacial molecular orientation on adhesion to plastics, the interfaces between poly(ethylene terephthalate) (PET) and different silane coupling agents were probed using sum frequency generation (SFG) vibrational spectroscopy. The polymer/air interface was dominated by the ester carbonyl, methylene, and phenyl groups. Upon contacting the PET film with the amino-functional silane 3-aminopropyltrimethoxysilane (ATMS), the ester carbonyl stretch shifted to a lower energy indicating the formation of hydrogen bonds between the polymer surface and the silane molecules. This shift was not observed when silanes that contained no hydrogen bond donors, such as (3-glycidoxypropyl)-trimethoxysilane and n-butyltrimethoxysilane, were placed into contact with the PET surface. Further evidence of silane ordering at the interface was observed as vibrational peaks attributed to the C-H stretching of the silane methoxy headgroups dominated the PET/silane spectra. It was determined that the conformation of the ATMS molecules at the interface was such that the amino endgroups were oriented toward the interface while the methoxy headgroups were directed toward the silane bulk.

Polarization Mapping: A Method To Improve Sum Frequency Generation Spectral Analysis

A "polarization mapping" method has been applied to improve the fitting quality of sum frequency generation (SFG) vibrational spectra of complicated systems and validate the data analysis of simple SFG spectra. Using such a method, two-dimensional SFG spectra can be constructed, from which more reliable spectral information can be obtained from a surface/interface. Model calculations as well as experiments have been employed to illustrate the power of the polarization mapping method for spectral analysis of SFG spectra. By using a deuterated polystyrene surface and interfacial protein molecules as examples, we demonstrate that this method is especially important for complicated molecules, such as polymers and proteins.