When the two end groups of a linear polymer chain are absorbed on a solid surface,the polymer chain forms the 'loop' conformation.Investigation has been made on the conformational statistics of a model loop ch...When the two end groups of a linear polymer chain are absorbed on a solid surface,the polymer chain forms the 'loop' conformation.Investigation has been made on the conformational statistics of a model loop chain by the normal landom walk (NRW) on a lattice confined in the half-infinite space.Based on the conformational distribution function of the NRW model tail chain,it is easy to deduce an analytical formula expressing the conforma-tional number of the model loop chain.It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power function N-2/3 when the chain length N→∞ The same result was obtained by means of the recursion equation.The ratio of the mean square end-to-end distance h2 for the model loop chain to its mean square bond length I2 is 2N/3 Compared with the free chain with the same length N,the mean square end-to-end distance of the model loop chain contracts to a certain extent.The basic relationships deduced were supported by the exact enumeration and Monte Garlo simulations.展开更多
The simplest form of a polymer chain adsorbed on a solid surface is that the polymer chain has only one end group attached to the surface, i.e. the polymer chain forms the "tail" conformation. In the present...The simplest form of a polymer chain adsorbed on a solid surface is that the polymer chain has only one end group attached to the surface, i.e. the polymer chain forms the "tail" conformation. In the present work, the problem was simplified as the random walk confined in the half-infinite space and studied systematically. The conformational distribution functions of the model tail chain in different dimensions were obtained. It has been found that the ratio of the conformational number of the model tail chains to that of the free chains varies as a power function N-12 when the chain length N→∞. It has also been proved that for the tail chain the component of the mean square end-to-end distance in the normal direction of the confined boundary is doubled and the other components are constant in comparison with the case of the free chain.展开更多
The SAW tail chains were studied.The permitted conformational number and the mean square end-to-end distance as a function of the chain length N for such a model tail chain were obtained by computer simulations,includ...The SAW tail chains were studied.The permitted conformational number and the mean square end-to-end distance as a function of the chain length N for such a model tail chain were obtained by computer simulations,including the exact enumeration and Monte Carlo method.These two basic quantities obeyed the relations deduced from the scaling law.The critical exponents and the lattice indexes were given by fitting the data of the computer experiments.It has been shown that there is a certain extension in the size of the SAW tail chains as well as the NRW tail chains in the direction normal to the wall.The normal component of the mean square end-to-end distance is almost twice as large as the parallel component of the short chain SAW.However,as N→∞,the effect of the wall on the chain conformation becomes a little weak because of the self-avoiding behavior for the model.That is quite different from the case of the NRW tail chain.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘When the two end groups of a linear polymer chain are absorbed on a solid surface,the polymer chain forms the 'loop' conformation.Investigation has been made on the conformational statistics of a model loop chain by the normal landom walk (NRW) on a lattice confined in the half-infinite space.Based on the conformational distribution function of the NRW model tail chain,it is easy to deduce an analytical formula expressing the conforma-tional number of the model loop chain.It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power function N-2/3 when the chain length N→∞ The same result was obtained by means of the recursion equation.The ratio of the mean square end-to-end distance h2 for the model loop chain to its mean square bond length I2 is 2N/3 Compared with the free chain with the same length N,the mean square end-to-end distance of the model loop chain contracts to a certain extent.The basic relationships deduced were supported by the exact enumeration and Monte Garlo simulations.
基金Project supported by the National Natural Science Foundation of China
文摘The simplest form of a polymer chain adsorbed on a solid surface is that the polymer chain has only one end group attached to the surface, i.e. the polymer chain forms the "tail" conformation. In the present work, the problem was simplified as the random walk confined in the half-infinite space and studied systematically. The conformational distribution functions of the model tail chain in different dimensions were obtained. It has been found that the ratio of the conformational number of the model tail chains to that of the free chains varies as a power function N-12 when the chain length N→∞. It has also been proved that for the tail chain the component of the mean square end-to-end distance in the normal direction of the confined boundary is doubled and the other components are constant in comparison with the case of the free chain.
基金supported by the National Natural Science Foundation of China
文摘The SAW tail chains were studied.The permitted conformational number and the mean square end-to-end distance as a function of the chain length N for such a model tail chain were obtained by computer simulations,including the exact enumeration and Monte Carlo method.These two basic quantities obeyed the relations deduced from the scaling law.The critical exponents and the lattice indexes were given by fitting the data of the computer experiments.It has been shown that there is a certain extension in the size of the SAW tail chains as well as the NRW tail chains in the direction normal to the wall.The normal component of the mean square end-to-end distance is almost twice as large as the parallel component of the short chain SAW.However,as N→∞,the effect of the wall on the chain conformation becomes a little weak because of the self-avoiding behavior for the model.That is quite different from the case of the NRW tail chain.
